SOERP computes second-order
error propagation equations for the first four moments of a
function of independently distributed random variables. SOERP was
written for a rigorous second-order error propagation of any
function which may be expanded in a multivariable Taylor series,
the input variables being independently distributed. The required
input consists of numbers directly related to the partial
derivatives of the function, evaluated at the nominal values of
the input variables and the central moments of the input variables
from the second through the eighth.

The development of equations for computing
the propagation of errors begins by expressing the function of
random variables in a multivariable Taylor series expansion. The
Taylor series expansion is then truncated, and statistical
operations are applied to the series in order to obtain equations
for the moments (about the origin) of the distribution of the
computed value. If the Taylor series is truncated after powers of
two, the procedure produces second-order error propagation
equations.